Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Generalized Fractional Integral Operators on Generalized Local Morrey Spaces Wed, 22 Apr 2015 06:23:08 +0000 We study the continuity properties of the generalized fractional integral operator on the generalized local Morrey spaces and generalized Morrey spaces . We find conditions on the triple which ensure the Spanne-type boundedness of from one generalized local Morrey space to another , , and from to the weak space , . We also find conditions on the pair which ensure the Adams-type boundedness of from to for and from to for . In all cases the conditions for the boundedness of are given in terms of Zygmund-type integral inequalities on and , which do not assume any assumption on monotonicity of , , and in . V. S. Guliyev, A. F. Ismayilova, A. Kucukaslan, and A. Serbetci Copyright © 2015 V. S. Guliyev et al. All rights reserved. Hardy-Littlewood-Sobolev Inequalities on -Adic Central Morrey Spaces Wed, 22 Apr 2015 06:19:59 +0000 We establish the Hardy-Littlewood-Sobolev inequalities on -adic central Morrey spaces. Furthermore, we obtain the -central BMO estimates for commutators of -adic Riesz potential on -adic central Morrey spaces. Qing Yan Wu and Zun Wei Fu Copyright © 2015 Qing Yan Wu and Zun Wei Fu. All rights reserved. Characterization Theorems for Generalized Functionals of Discrete-Time Normal Martingale Sun, 19 Apr 2015 10:42:18 +0000 We aim at characterizing generalized functionals of discrete-time normal martingales. Let be a discrete-time normal martingale that has the chaotic representation property. We first construct testing and generalized functionals of with an appropriate orthonormal basis for ’s square integrable functionals. Then we introduce a transform, called the Fock transform, for these functionals and characterize them via the transform. Several characterization theorems are established. Finally we give some applications of these characterization theorems. Our results show that generalized functionals of discrete-time normal martingales can be characterized only by growth condition, which contrasts sharply with the case of some continuous-time processes (e.g., Brownian motion), where both growth condition and analyticity condition are needed to characterize generalized functionals of those continuous-time processes. Caishi Wang and Jinshu Chen Copyright © 2015 Caishi Wang and Jinshu Chen. All rights reserved. Some Classes of Function Spaces, Their Properties, and Their Applications 2014 Wed, 08 Apr 2015 06:56:05 +0000 Józef Banaś, Janusz Matkowski, Nelson Merentes, Jose Luis Sanchez, and Kishin Sadarangani Copyright © 2015 Józef Banaś et al. All rights reserved. Multiplication Operator with BMO Symbols and Berezin Transform Mon, 06 Apr 2015 11:50:09 +0000 We discuss multiplication operator with a special symbol on the weighted Bergman space of the unit ball. We give the necessary and sufficient conditions for the compactness of multiplication operator on the weighted Bergman space of the unit ball. Xue Feng, Kan Zhang, Jianguo Dong, Xianmin Liu, and Chi Guan Copyright © 2015 Xue Feng et al. All rights reserved. Functions Like Convex Functions Mon, 06 Apr 2015 11:25:50 +0000 The paper deals with convex sets, functions satisfying the global convexity property, and positive linear functionals. Jensen's type inequalities can be obtained by using convex combinations with the common center. Following the idea of the common center, the functional forms of Jensen's inequality are considered in this paper. Zlatko Pavić Copyright © 2015 Zlatko Pavić. All rights reserved. Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies Mon, 06 Apr 2015 11:09:39 +0000 Let be a completely regular Hausdorff space, and let and be Banach spaces. Let be the space of all -valued bounded, continuous functions defined on , equipped with the strict topologies , where . General integral representation theorems of -continuous linear operators with respect to the corresponding operator-valued measures are established. Strongly bounded and -continuous operators are studied. We extend to “the completely regular setting” some classical results concerning operators on the spaces and , where is a compact or a locally compact space. Marian Nowak Copyright © 2015 Marian Nowak. All rights reserved. Positive Solutions for a Class of Singular Boundary Value Problems with Fractional -Difference Equations Mon, 06 Apr 2015 11:07:16 +0000 We discuss a class of singular boundary value problems of fractional -difference equations. Some existence and uniqueness results are obtained by a fixed point theorem in partially ordered sets. Finally, we give an example to illustrate the results. Jufang Wang, Changlong Yu, and Yanping Guo Copyright © 2015 Jufang Wang et al. All rights reserved. Properties of Functions in the Wiener Class for Mon, 06 Apr 2015 09:23:31 +0000 We will investigate properties of functions in the Wiener class with . We prove that any function in can be expressed as the difference of two increasing functions in . We also obtain the explicit form of functions in and show that their derivatives are equal to zero a.e. on . Yeli Niu and Heping Wang Copyright © 2015 Yeli Niu and Heping Wang. All rights reserved. Simultaneous Approximation for Generalized Srivastava-Gupta Operators Mon, 06 Apr 2015 09:23:23 +0000 We introduce a new Stancu type generalization of Srivastava-Gupta operators to approximate integrable functions on the interval and estimate the rate of convergence for functions having derivatives of bounded variation. Also we present simultenaous approximation by new operators in the end of the paper. Tuncer Acar, Lakshmi Narayan Mishra, and Vishnu Narayan Mishra Copyright © 2015 Tuncer Acar et al. All rights reserved. Decompositions of -Frames and Duals and Pseudoduals of -Frames in Hilbert Spaces Mon, 06 Apr 2015 09:11:46 +0000 Firstly, we study the representation of -frames in terms of linear combinations of simpler ones such as -orthonormal bases, -Riesz bases, and normalized tight -frames. Then, we study the dual and pseudodual of -frames, which are critical components in reconstructions. In particular, we characterize the dual -frames in a constructive way; that is, the formulae for dual -frames are given. We also give some -frame like representations for pseudodual -frame pairs. The operator parameterizations of -frames and decompositions of bounded operators are the key tools to prove our main results. Xunxiang Guo Copyright © 2015 Xunxiang Guo. All rights reserved. Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces Mon, 06 Apr 2015 08:47:14 +0000 Let be the infinitesimal generator of an analytic semigroup on with Gaussian kernel bounds, and let be the fractional integrals of for . Assume that is a finite family of locally integrable functions; then the multilinear commutators generated by and are defined by . Assume that belongs to weighted BMO space, ; the authors obtain the boundedness of on weighted Morrey spaces. As a special case, when is the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutator on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results. Sha He, Taotao Zheng, and Xiangxing Tao Copyright © 2015 Sha He et al. All rights reserved. Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators Mon, 06 Apr 2015 08:44:59 +0000 Let be a Schrödinger operator on , where is a nonnegative potential belonging to the reverse Hölder class . The Hardy type spaces for some , are defined in terms of the maximal function with respect to the semigroup . In this paper, we investigate the bounded properties of some singular integral operators related to , such as and , on spaces . We give the molecular characterization of , which is used to establish the -boundedness of singular integrals. Jianfeng Dong, Jizheng Huang, and Heping Liu Copyright © 2015 Jianfeng Dong et al. All rights reserved. Limit Cycles and Analytic Centers for a Family of Degree Systems with Generalized Nilpotent Singularities Mon, 06 Apr 2015 08:10:31 +0000 With the aid of computer algebra system Mathematica 8.0 and by the integral factor method, for a family of generalized nilpotent systems, we first compute the first several quasi-Lyapunov constants, by vanishing them and rigorous proof, and then we get sufficient and necessary conditions under which the systems admit analytic centers at the origin. In addition, we present that seven amplitude limit cycles can be created from the origin. As an example, we give a concrete system with seven limit cycles via parameter perturbations to illustrate our conclusion. An interesting phenomenon is that the exponent parameter controls the singular point type of the studied system. The main results generalize and improve the previously known results in Pan. Yusen Wu, Cui Zhang, and Changjin Xu Copyright © 2015 Yusen Wu et al. All rights reserved. The Improvement on the Boundedness and Norm of a Class of Integral Operators on Space Mon, 06 Apr 2015 07:56:03 +0000 We prove the condition “ is neither nor a negative integer” can be dropped on the boundedness of a class of integral operators on space, which improves the result by Krues and Zhu. Besides, the exact norm of on space is also obtained under the assumption . Lifang Zhou and Jin Lu Copyright © 2015 Lifang Zhou and Jin Lu. All rights reserved. Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations Mon, 06 Apr 2015 07:35:30 +0000 The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role. In this paper, we investigate the Cauchy problem of the three-dimensional incompressible Boussinesq equations. By commutator estimate, some interpolation inequality, and embedding theorem, we establish a blow-up criterion of weak solutions in terms of the pressure in the homogeneous Besov space . Zhaohui Dai, Xiaosong Wang, Lingrui Zhang, and Wei Hou Copyright © 2015 Zhaohui Dai et al. All rights reserved. Herz-Morrey-Hardy Spaces with Variable Exponents and Their Applications Mon, 06 Apr 2015 07:08:21 +0000 The authors introduce Herz-Morrey-Hardy spaces with variable exponents and establish the characterization of these spaces in terms of atom. Applying the characterization, the authors obtain the boundedness of some singular integral operators on these spaces. Jingshi Xu and Xiaodi Yang Copyright © 2015 Jingshi Xu and Xiaodi Yang. All rights reserved. Singularities of Null Hypersurfaces of Pseudonull Curves Tue, 31 Mar 2015 14:21:01 +0000 The main goal of this paper is to study the singularities of null hypersurfaces of pseudonull curves. To do this we construct a null frame and a Lorentz distance-squared function of the pseudonull curve. The relations are shown between singularities of the null hypersurfaces and those, of the Lorentz distance-squared function. And we reveal the geometric meanings of the singularities of such hypersurfaces. In addition, we also introduce some properties of the nullcone Gaussian surface of the pseudonull curve. Xiupeng Cui and Donghe Pei Copyright © 2015 Xiupeng Cui and Donghe Pei. All rights reserved. On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space Mon, 30 Mar 2015 13:52:16 +0000 We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion. Irene Benedetti, Valeri Obukhovskii, and Valentina Taddei Copyright © 2015 Irene Benedetti et al. All rights reserved. Variational Inequalities with Multivalued Lower Order Terms and Convex Functionals in Orlicz-Sobolev Spaces Wed, 25 Mar 2015 13:02:54 +0000 We consider the existence of solutions of variational inequality form. Find , whose principal part is having a growth not necessarily of polynomial type, where is a second-order elliptic operator of Leray-Lions type, is a multivalued lower order term, and is a convex functional. We use subsupersolution methods to study the existence and enclosure of solutions in Orlicz-Sobolev spaces. Ge Dong and Xiaochun Fang Copyright © 2015 Ge Dong and Xiaochun Fang. All rights reserved. Three-Point Boundary Value Problems for Conformable Fractional Differential Equations Wed, 18 Mar 2015 15:40:13 +0000 We study a fractional differential equation using a recent novel concept of fractional derivative with initial and three-point boundary conditions. We first obtain Green's function for the linear problem and then we study the nonlinear differential equation. H. Batarfi, Jorge Losada, Juan J. Nieto, and W. Shammakh Copyright © 2015 H. Batarfi et al. All rights reserved. New Set-Valued Integral in a Banach Space Mon, 16 Mar 2015 13:52:29 +0000 We introduce and study a new set-valued integral of scalar-valued functions with respect to a set-valued measure in a Banach space. We investigate some properties and convergence theorems for this kind of integral. Cai-Li Zhou and Fu-Gui Shi Copyright © 2015 Cai-Li Zhou and Fu-Gui Shi. All rights reserved. On the Null Space Property of -Minimization for in Compressed Sensing Mon, 16 Mar 2015 10:03:16 +0000 The paper discusses the relationship between the null space property (NSP) and the -minimization in compressed sensing. Several versions of the null space property, that is, the stable NSP, the robust NSP, and the robust NSP for based on the standard NSP, are proposed, and their equivalent forms are derived. Consequently, reconstruction results for the -minimization can be derived easily under the NSP condition and its equivalent form. Finally, the NSP is extended to the -synthesis modeling and the mixed -minimization, which deals with the dictionary-based sparse signals and the block sparse signals, respectively. Yi Gao, Jigen Peng, Shigang Yue, and Yuan Zhao Copyright © 2015 Yi Gao et al. All rights reserved. A Subordination Principle on Wright Functions and Regularized Resolvent Families Mon, 16 Mar 2015 06:53:25 +0000 We obtain a vector-valued subordination principle for -regularized resolvent families which unified and improves various previous results in the literature. As a consequence, we establish new relations between solutions of different fractional Cauchy problems. To do that, we consider scaled Wright functions which are related to Mittag-Leffler functions, the fractional calculus, and stable Lévy processes. We study some interesting properties of these functions such as subordination (in the sense of Bochner), convolution properties, and their Laplace transforms. Finally we present some examples where we apply these results. Luciano Abadias and Pedro J. Miana Copyright © 2015 Luciano Abadias and Pedro J. Miana. All rights reserved. Space of -Periodic Limit Functions and Its Applications to an Abstract Cauchy Problem Sun, 15 Mar 2015 07:05:47 +0000 We introduce a new space consisting of what we call -periodic limit functions. We investigate some properties of the new function space. In particular, we study inclusion relations among asymptotically periodic type function spaces. Finally, we apply the -periodic limit functions to investigate the existence and uniqueness of asymptotically -periodic mild solutions of an abstract Cauchy problem. Rui Xie and Chuanyi Zhang Copyright © 2015 Rui Xie and Chuanyi Zhang. All rights reserved. Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball Wed, 11 Mar 2015 10:52:23 +0000 We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory. Alma García and Nikolai Vasilevski Copyright © 2015 Alma García and Nikolai Vasilevski. All rights reserved. A Reverse Theorem on the - Continuity of the Dual Map Tue, 10 Mar 2015 09:12:39 +0000 Given a Banach space , , and , we define the set of all for which there exist two sequences and such that converges to , has a subnet -convergent to , and for all . We prove that if is separable and reflexive and enjoys the Radon-Riesz property, then is contained in the boundary of relative to . We also show that if is infinite dimensional and separable, then there exists an equivalent norm on such that the interior of relative to is contained in . Mienie de Kock and Francisco Javier García-Pacheco Copyright © 2015 Mienie de Kock and Francisco Javier García-Pacheco. All rights reserved. The Singular Points of Analytic Functions with Finite -Order Defined by Laplace-Stieltjes Transformations Mon, 02 Mar 2015 06:54:36 +0000 We study the singular points of analytic functions defined by Laplace-Stieltjes transformations which converge on the right half plane, by introducing the concept of -order functions. We also confirm the existence of the finite -order Borel points of such functions and obtained the extension of the finite -order Borel point of two analytic functions defined by two Laplace-Stieltjes transformations convergent on the right half plane. The main results of this paper are improvement of some theorems given by Shang and Gao. Hong-Yan Xu and Zu-Xing Xuan Copyright © 2015 Hong-Yan Xu and Zu-Xing Xuan. All rights reserved. Jordan Type Inequalities for Hyperbolic Functions and Their Applications Sun, 01 Mar 2015 14:16:04 +0000 We present the best possible parameters p, such that the double inequality holds for all . As applications, some new inequalities for certain special function and bivariate means are found. Zhen-Hang Yang and Yu-Ming Chu Copyright © 2015 Zhen-Hang Yang and Yu-Ming Chu. All rights reserved. Existence and Asymptotic Behaviour of Solutions of Differential and Integral Equations in Some Function Spaces Sun, 01 Mar 2015 10:25:40 +0000 Józef Banaś, Mohamed Abdalla Darwish, Leszek Olszowy, and Kishin Sadarangani Copyright © 2015 Józef Banaś et al. All rights reserved.